
from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any

@dataclass
class 							_UpperCamelCase					:






			'''simple docstring'''

			__UpperCamelCase   :    int
			__UpperCamelCase   :    Node | None          =			None
			__UpperCamelCase   :    Node | None          =			None







def 							A__       (    )	->						Node | None:
				UpperCamelCase_:				str						=    Node(1    )
				UpperCamelCase_:				Tuple						=    Node(2    )
				UpperCamelCase_:				Union[str, Any]						=    Node(3    )
				UpperCamelCase_:				int						=    Node(4    )
				UpperCamelCase_:				Optional[Any]						=    Node(5    )
				return tree







def 							A__       (    lowerCamelCase    )	->						list[int]:
				return [root.data, *preorder(root.left    ), *preorder(root.right    )] if root else []







def 							A__       (    lowerCamelCase    )	->						list[int]:
				return postorder(root.left    ) + postorder(root.right    ) + [root.data] if root else []







def 							A__       (    lowerCamelCase    )	->						list[int]:
				return [*inorder(root.left    ), root.data, *inorder(root.right    )] if root else []







def 							A__       (    lowerCamelCase    )	->						int:
				return (max(height(root.left    )  ,     height(root.right    )    ) + 1) if root else 0







def 							A__       (    lowerCamelCase    )	->						Sequence[Node | None]:
				UpperCamelCase_:				list[Any]						=    []

				if root is None:
								return output

				UpperCamelCase_:				List[Any]						=    deque([root]    )

				while process_queue:
								UpperCamelCase_:				Union[str, Any]						=    process_queue.popleft()
								output.append(node.data    )

								if node.left:
												process_queue.append(node.left    )
								if node.right:
												process_queue.append(node.right    )
				return output







def 							A__       (    lowerCamelCase  ,     lowerCamelCase    )	->						Sequence[Node | None]:
				UpperCamelCase_:				list[Any]						=    []

				def populate_output(lowerCamelCase  ,     lowerCamelCase    ) -> None:
								if not root:
												return
								if level == 1:
												output.append(root.data    )
								elif level > 1:
												populate_output(root.left  ,     level - 1    )
												populate_output(root.right  ,     level - 1    )

				populate_output(lowerCamelCase  ,     lowerCamelCase    )
				return output







def 							A__       (    lowerCamelCase  ,     lowerCamelCase    )	->						Sequence[Node | None]:
				UpperCamelCase_:				list[Any]						=    []

				def populate_output(lowerCamelCase  ,     lowerCamelCase    ) -> None:
								if root is None:
												return
								if level == 1:
												output.append(root.data    )
								elif level > 1:
												populate_output(root.right  ,     level - 1    )
												populate_output(root.left  ,     level - 1    )

				populate_output(lowerCamelCase  ,     lowerCamelCase    )
				return output







def 							A__       (    lowerCamelCase    )	->						Sequence[Node | None] | list[Any]:
				if root is None:
								return []

				UpperCamelCase_:				list[Sequence[Node | None]]						=    []

				UpperCamelCase_:				List[Any]						=    0
				UpperCamelCase_:				Optional[int]						=    height(lowerCamelCase    )

				for h in range(1  ,     height_tree + 1    ):
								if not flag:
												output.append(get_nodes_from_left_to_right(lowerCamelCase  ,     lowerCamelCase    )    )
												UpperCamelCase_:				Dict						=    1
								else:
												output.append(get_nodes_from_right_to_left(lowerCamelCase  ,     lowerCamelCase    )    )
												UpperCamelCase_:				int						=    0

				return output







def 							A__       (    )	->						None:  # Main function for testing.
				UpperCamelCase_:				int						=    make_tree()
				print(F'''In-order Traversal: {inorder(lowerCamelCase    )}'''    )
				print(F'''Pre-order Traversal: {preorder(lowerCamelCase    )}'''    )
				print(F'''Post-order Traversal: {postorder(lowerCamelCase    )}'''  ,     """\n"""    )

				print(F'''Height of Tree: {height(lowerCamelCase    )}'''  ,     """\n"""    )

				print("""Complete Level Order Traversal: """    )
				print(level_order(lowerCamelCase    )  ,     """\n"""    )

				print("""Level-wise order Traversal: """    )

				for level in range(1  ,     height(lowerCamelCase    ) + 1    ):
								print(F'''Level {level}:'''  ,     get_nodes_from_left_to_right(lowerCamelCase  ,     level=lowerCamelCase    )    )

				print("""\nZigZag order Traversal: """    )
				print(zigzag(lowerCamelCase    )    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()








from __future__ import annotations







def 							A__       (    lowerCamelCase    )	->						int:
				UpperCamelCase_:				Optional[Any]						=    len(lowerCamelCase    ) // 2

				# choose the middle 3 elements
				UpperCamelCase_:				Tuple						=    lst[m - 1 : m + 2]

				# if middle element is peak
				if three[1] > three[0] and three[1] > three[2]:
								return three[1]

				# if increasing, recurse on right
				elif three[0] < three[2]:
								if len(lst[:m]    ) == 2:
												m -= 1
								return peak(lst[m:]    )

				# decreasing
				else:
								if len(lst[:m]    ) == 2:
												m += 1
								return peak(lst[:m]    )


if __name__ == "__main__":
							import doctest

							doctest.testmod()






